Exam 14: Numerical Methods

The regula falsi root-finding method is essentially the same as bisection, except instead of using the interval s midpoint at each step of the calculation, you use a(n) ____ value for the root.

The ____ method is probably the most popular method for finding the root of a function.

The ____ root-finding method uses a predictable number of iterations.

Using the ____ root-finding method, the interval is made to collapse from both directions.

____ rule is based on approximating a function by parabolic segments.

Specifying a parabola uniquely requires ____ points.

A straight line is the simplest approximation to a function.

By using information about the ____ of a functional value in addition to its sign, you can speed up the convergence of your root-finding scheme.

One of the most common tasks in science and engineering is finding the roots of equations.

A polynomial of degree n has precisely ____ roots.

In the ____ method, you can predict with some precision the number of iterations required to find a function s root to a certain accuracy.

The lowest-order Simpson s rule has ____ panel(s).

Many of the theorems you learned for roots of polynomials don t apply to transcendental equations.

In numerical integration, excessive ____________________ times is a potential problem.

A root-finding method that uses a minimum of finesse is known as a ____ method.

____________________ error occurs when the values of f ( x 1) and f ( x 3) used in the computation are nearly equal.

Among the bisection, regula falsi, and modified regula falsi methods, the ____ method is probably the most efficient for common problems.

An approximation to the area under a complicated curve is obtained by assuming the function can be replaced by simpler functions over a limited range.

With the regula falsi method of root-finding, success is based on the size of the function, not the size of the interval.

____ consists of expressing the area as the sum of areas of smaller segments.